Part A: Find a rational number that is between 5.2 and 5.5, Explain why it is rational. (2 points)
Find an irrational number that is between 5.2 and 5.5. Explain why it is irrational. Include the decimal approximation of the irrational number to the
nearest hundredth.
Answers
9514 1404 393
Answer:
A. 5.3
B. √29 ≈ 5.39
Step-by-step explanation:
A.A terminating decimal is a rational number. A terminating decimal between 5.2 and 5.5 is 5.3.
__
B.The squares of 5.2 and 5.5 are 27.04 and 30.25, respectively. Any value between these numbers that is not a perfect square will have an irrational square root. For example, √29 ≈ 5.39 is irrational.
Answer:
Step-by-step explanation:
Part A
5.3
This is rational because it can be represented as 53/10
5 3/10
5 * 10 + 3 / 10
(50 + 3) / 10
53/10 which is a rational fraction.
Part B
You want something irrational between 5.2 and 5.5. You can take the square root of something like sqrt(29.16) which is 5.4 squared.
To make it irrational just add a small amount to 29.16 which would be .02 tp get 29.18
Square root 29.18 = 5.401851534
This is irrational because you cannot represent the number as a fraction. You can test the notion by asking what the next digit after 34 at the end is. You have no better that a 1 in 10 chance of getting it right. Did you guess 4? If you did, that was just luck. Here is a more complete square root, but still not rational.
5.4018515344278020984773871207007
If you are using windows on your computer, this number comes from the calculator that is included with windows. What comes after 007? I don't have a way of telling you. The result is irrational.
Related Questions
-4.3 + x equals 0 selected place on the number line to positive value of x
Answers
Answer:
x is equal to 4.3
Step-by-step explanation:
since it's -4.3 + x is equal to 0
you take -4.3 to the other side of the equal sign which makes it positive and x is equal to 4.3
You have 10 grades in your math class. After ordering them from least to greatest, this is the data set: {80, 82, 82, 83, 85, 88, 92, 95, 95, 96}. Which statement is true about the mode?
The mode is 95.
The mode is 82.
There are two modes: 82 and 95.
There is no mode
Answers
Answer:
82 and 95
Step-by-step explanation:
Most repeated
consider the value of t such that the area to the left of −|t|−|t| plus the area to the right of |t||t| equals 0.10.1.
Answers
We want to find the value of t such that the area to the left of −|t| plus the area to the right of |t| equals 0.1.
That is level of significance (α) = two-tail area = 0.1
what is a level of significance in research?
The significance stage (also called kind I mistakes rate or the extent of statistical importance) refers back to the chance of rejecting a null hypothesis that is in truth true. This amount stages from 0 (0.0) to at least one (1.zero) and is generally denoted through the Greek letter alpha (a).
What are the three levels of significance?
commonplace importance stages are 0.10 (1 risk in 10), 0.05 (1 risk in 20), and zero.01 (1 hazard in one hundred). The result of a speculation check, as has been seen, is that the null hypothesis is both rejected or now not.
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The given planes intersect in a line. Find parametric equations for the line of intersection. [Hint: The line of intersection consists of all points (x, y, z) that satisfy both equations. Solve the system and designate the unconstrained variable as t .]
x + 2y + z = 1, 2x+5y + 32 = 4
Answers
The parametric equations for the line of intersection are:
x = 61 - 5t
y = 2t - 30
z = t
To find the parametric equations for the line of intersection of the given planes, we first need to solve the system of equations:
1. x + 2y + z = 1
2. 2x + 5y + 32 = 4
Step 1: Solve for x from equation 1:
x = 1 - 2y - z
Step 2: Substitute x in equation 2 with the expression found in step 1:
2(1 - 2y - z) + 5y + 32 = 4
Now we can use elimination to solve for one variable. Let's eliminate y by multiplying the first equation by 5 and subtracting it from the second equation:
Step 3: Simplify and solve for y:
2 - 4y - 2z + 5y + 32 = 4
y - 2z = -30
Step 4: Designate z as the parameter t:
z = t
Step 5: Substitute z with t in the expression for y:
y = 2t - 30
Step 6: Substitute z with t in the expression for x:
x = 1 - 2(2t - 30) - t
x = 1 - 4t + 60 - t
x = 61 - 5t
Now we have the parametric equations for the line of intersection:
x = 61 - 5t
y = 2t - 30
z = t
Note that we can choose any value of z for the parameter t, since z is unconstrained.
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Suppose a research repot has estmated the demand for a frm's prodact as in O
X
d
=7−15 in P
X
+2 in Py=05 in M+ in A where:
P
X
=$15
P
y
=$6
M−$40000, and
A=$350
a Determine the ownt price elasticity of demand, and state whether demard is elassc, inelastic, ar untary elartic: Own price elasticty Demand is b. Determine Bre cross-pice elasticfy of demand between good X and goed Y, and state whetfer these two goods are sibstitutes or campleinents. Cross gnice efasticfly These two goods are: C. Determine the income elasticity of demand, and state whesher good X1 s a normal or inferior good. lncome elassicity? Good X is: 4. Determine the own advertising elasticity of demand.
Answers
a. Own Price Elasticity of Demand = (-30) / (0) = undefined. Since the own price elasticity of demand is undefined, we cannot determine if the demand is elastic, inelastic, or unitary elastic based on this information.
b. Cross-Price Elasticity of Demand = (12/7) / 0 = undefined. Since the cross-price elasticity of demand is undefined, we cannot determine if goods X and Y are substitutes or complements based on this information.
c. Income Elasticity of Demand = (-2860.71) / (0) = undefined. Since the income elasticity of demand is undefined, we cannot determine if good X is a normal or inferior good based on this information.
d. We cannot calculate the own advertising elasticity of demand with the provided data.
a. To determine the own price elasticity of demand, we need to use the formula:
Own Price Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Price)
Given the demand equation OXd = 7−15PX+2Py+0.5M+A, we can calculate the derivative of demand with respect to price:
d(OXd) / d(PX) = -15
Now, let's plug in the values:
% Change in Quantity Demanded = (d(OXd) / d(PX)) * (PX / OXd) = (-15) * (15 / 7) = -30
% Change in Price = (ΔPX / PX) = (15 - 15) / 15 = 0
b. To determine the cross-price elasticity of demand between goods X and Y, we use the formula:
Cross-Price Elasticity of Demand = (% Change in Quantity Demanded of Good X) / (% Change in Price of Good Y)
Using the same demand equation, we calculate the derivative of demand with respect to the price of good Y:
d(OXd) / d(Py) = 2
Now, let's plug in the values:
% Change in Quantity Demanded of Good X = (d(OXd) / d(Py)) * (Py / OXd) = (2) * (6 / 7) = 12/7
% Change in Price of Good Y = (ΔPy / Py) = (6 - 6) / 6 = 0
c. To determine the income elasticity of demand, we use the formula:
Income Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Income)
Using the same demand equation, we calculate the derivative of demand with respect to income:
d(OXd) / d(M) = 0.5
Now, let's plug in the values:
% Change in Quantity Demanded = (d(OXd) / d(M)) * (M / OXd) = (0.5) * (-40000 / 7) = -2860.71
% Change in Income = (ΔM / M) = (-40000 - (-40000)) / (-40000) = 0
d. The own advertising elasticity of demand measures the responsiveness of quantity demanded to changes in advertising expenditure. Unfortunately, the given demand equation does not provide any information about advertising expenditure or its impact on quantity demanded.
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alex wants to fence in an area for a dog park. he has plotted three sides of the fenced area at the points e (1, 5), f (3, 5), and g (6, 1). he has 16 units of fencing. where could alex place point h so that he does not have to buy more fencing?
Answers
The point H could be (1 + √134.56, 5) or (1 - √134.56, 5).
Let’s plot the given points E, F and G on the graph and try to find the missing point H:
Now, the length of the side EF will be:
EF = √((3-1)² + (5-5)²)EF = 2 units
The length of the side FG will be:
FG = √((6-3)² + (1-5)²)FG = √10 units
The length of the side EG will be:
EG = √((6-1)² + (1-5)²)EG = √26 units
Therefore, the total length of the three sides of the fence will be:2 + √10 + √26 units
Now, the perimeter of the fenced area with 4 sides EFGH is:16 = 2 + √10 + √26 + EHThe length of EH will be:
EH = 16 - 2 - √10 - √26EH = 11.60 units
We need to plot the missing point H which is at a distance of 11.60 units from point E along the line passing through points E and F.
Using the slope formula we find that the slope of the line passing through points E and F is: m = (y2 - y1)/(x2 - x1) = (5 - 5)/(3 - 1) = 0Therefore the line passing through E and F is a horizontal line as it has zero slope.
The distance between points E and H is 11.60 units and point H will be on the same horizontal line passing through E and F.Therefore, the x-coordinate of point H will be:
EH = √((x2-x1)² + (y2-y1)²)11.60 = √((x-1)² + (5-5)²)
Solving the above equation:
(x-1)² = 134.56(x-1)
= ±√134.56x
= 1 + √134.56 or x = 1 - √134.56
Therefore, the point H could be (1 + √134.56, 5) or (1 - √134.56, 5).
Point H could be (1 + √134.56, 5) or (1 - √134.56, 5).
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Create ABC by drawing AC. AC represents the foreman’s line of sight to the top of the landfill. What is m
Answers
Where the above is given, the required angle m∠BAC = 45°.
In triangle ABC. AC represents the foreman’s line of sight to the top of the landfill. Landfill height is BC
What is triangle?The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°
According to conditions angle b = 90°
The sum of angles of a triangle= 180°
That is a + b + c = 180
Therefore, c = a
a = (180 - b)/2
= (180 - 90) / 2
= 90 / 2
= 45°
Hence, the required angle m∠BAC = 45°
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Question 1 Create Triangle ABC by drawing AC. Segment AC represents the foreman’s line of sight to the top of the landfill. What is Angle m BAC?
Which inequality describes the possible values of x?
B
F
12
50°
с
E
G
(5x-10)
10
D
A. 2
O
B. 2
C. 2
D. 2 < x < 22
Answers
Answer:
Step-by-step explanation:
ive done this before and the answer to the equation is c and also truss me on this if you want. I wouldnt
The inequality that describes the possible value of x is 2< x < 22.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.
Given that ∠A = 50°
AB ≈ DE ≈ EF
BC = 12
CD = 10
And the ∠E = (5x - 10)°
From the Graph, we can see that Angle A is the alternate angle to angle G
Alternate angles are the angles that occur on opposite sides of the transversal line. We can easily spot two interior alternate angles by drawing Z. The value of alternate angles is equal.
thus, ∠A = ∠E
50° = 5x -10
5x = 60
x = 12
Therefore, from the given options the value of x lies in the inequality 2 < x < 22.
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A hose is used to fill up a 1,200 gallon water truck. Water flows form the hose at a constant rate. After 10 minutes, there are 65 gallons of water in the truck. After 15 minutes there are 82 gallons of water in the truck. How long will it take to fill up the truck?
Answers
Answer:
The time it would take to fill up the truck is approximately 344 minutes
Step-by-step explanation:
The given parameters of the truck are;
The volume of the water truck, V = 1,200 gallon
The rate at which water flows from the hose. m = Constant rate
The volume of water in the truck after t₁ = 10 minutes is V₁ = 65 gallons
The volume of water in the truck after t₂ = 15 minutes is V₂ = 82 gallons
Therefore, the rate at which water flows from the hose to the truck, 'm', is given by the equation for the slope of a straight (constant variation) line, as follows;
\(m = \dfrac{V_2 - V_1}{t_2 - t_1}\)
Therefore, we have;
\(m = \dfrac{82 \, gallons - 65 \, gallons}{15 \, minutes - 10 \, minutes} = 3.4 \, gallons/minute\)
The point and slope form of the straight line equation relationship between the volume in the tank and the time of flow is given as follows;
V - 82 = 3.4 × (t - 15)
Therefore, the slope and intercept form of the equation is given as follows;
V = 3.4·t - 15 × 3.4 + 82 = 3.4·t + 31
∴ V = 3.4·t + 31
When the tank is filled, V = 1,200 gallons, therefore, we have;
1,200 = 3.4·t + 31
3.4·t = 1,200 - 31 = 1,169
t = 1,169/3.4 = 5845/17 = 343.\(\overline{8235294117647058}\)
The time it would take to fill up the truck, t = 343.\(\overline{8235294117647058}\) minutes ≈ 344 minutes.
Santos takes the train into the city five days a week for work. For one work week he kept track of how many minutes the train ride was : 48,51,48,48,50
Calculate the mean median range in the range of the train ride times for the week
Answers
The mean train ride time for the week was 49.4 minutes, with a median of 48 minutes. The range of the train ride times was 3 minutes.
The mean, median, and range of Santos' train ride times for the week were as follows:
Mean: 49.4 minutes
The mean is calculated by adding up all the values and dividing the sum by the total number of values. In this case, the sum of the train ride times (48 + 51 + 48 + 48 + 50) is 245 minutes. Dividing this sum by the total number of days (5), we get the mean of 49.4 minutes.
Median: 48 minutes
The median is the middle value in a sorted list of numbers. To find the median, we arrange the train ride times in ascending order: 48, 48, 48, 50, 51. Since there is an odd number of values, the middle value is the median. In this case, the median is 48 minutes.
Range: 3 minutes
The range is the difference between the largest and smallest values in a set. To calculate the range, we subtract the smallest value (48 minutes) from the largest value (51 minutes). In this case, the range of the train ride times for the week is 3 minutes.
In summary, the mean train ride time for the week was 49.4 minutes, with a median of 48 minutes. The range of the train ride times was 3 minutes. These metrics provide insights into the average, central tendency, and variability of Santos' train rides throughout the week.
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express the integral ∭ef(x,y,z)dv as an iterated integral in six different ways, where e is the solid bounded by z=0,x=0,z=y−4x and y=12.
Answers
These six different iterated integrals represent the same volume integral but with different orders of integration.
What are the six different ways to express the integral of a solid bounded by given planes as an iterated integral?To express the integral ∭ef(x,y,z)dv as an iterated integral in six different ways, where e is the solid bounded by
z=0, x=0, z=y-4x,
and y=12, we first determine the limits of integration for each variable. The solid is bounded by the following planes:
z = 0 (lower limit for z)
x = 0 (lower limit for x)
z = y - 4x (upper limit for z)
y = 12 (upper limit for y)
Now, we can write the iterated integral in six different orders of integration:
dx dy dz:
∭ef(x,y,z)dv = ∫(0 to 12)∫(0 to y/4)∫(0 to y-4x) ef(x,y,z) dz dx dy
dx dz dy:
∭ef(x,y,z)dv = ∫(0 to 12)∫(0 to y-4x)∫(0 to y/4) ef(x,y,z) dx dz dy
dy dx dz:
∭ef(x,y,z)dv = ∫(0 to 12)∫(0 to y/4)∫(0 to y-4x) ef(x,y,z) dz dy dx
dy dz dx:
∭ef(x,y,z)dv = ∫(0 to 12)∫(0 to y-4x)∫(0 to y/4) ef(x,y,z) dy dz dx
dz dx dy:
∭ef(x,y,z)dv = ∫(0 to 12)∫(0 to y/4)∫(0 to y-4x) ef(x,y,z) dx dy dz
dz dy dx:
∭ef(x,y,z)dv = ∫(0 to 12)∫(0 to y-4x)∫(0 to y/4) ef(x,y,z) dy dx dz
These six different iterated integrals represent the same volume integral but with different orders of integration.
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What is the area of the figure?
PLEASE HELP ILL GIVE BRAINLIEST TO FIRST PERSON WHO GETS IT RIGHT
Answers
Answer:
112in^2
Step-by-step explanation:
area of square = 10*10
= 100in
area of triangle = (6*4)/2
= 12in
100+12= 112
area of shape = 112in
Answer:
The area of the figure is 112
Step-by-step explanation:
For area, you multiply length x width
For the triangle, you do HALF THE BASE x height
So for the square, it's fairly simple
10 x 10 = 100
For the triangle, it's a bit more complicated
So we know the length of the square is 10 inches
And we see a 6 inch mark at the top of the square, showing where the square ends and the triangle begins
So the base of the triangle is 10 - 6 = 4 inches
Also, the overall height of the figure is 16 inches, and the height of the square is 10 inches
So the height of the triangle is 16 - 10 = 6 inches
So 4 is the base of the triangle
And 6 is the height of the triangle
So we half 4, which gives us 2
2 x 6 = 12
The area of the triangle is 12
And we already determined that the area of the square is 100
100 + 12 = 112
The area of the whole figure is 112
Use: nCk = n!/k! (n-k)!
At a local cafeteria there are ten vegetable selections available. How many three-vegetable plates may be made
Answers
Answer:
120
Step-by-step explanation:
The formula \(nCk=\frac{n!}{k!(n-k)!}\) describes how many ways \(k\) items can be chosen given \(n\) total items. In this scenario, \(n=10\), and \(k=3\), thus:
\(\frac{10!}{3!(10-3)!}=120\)
This means that you can make 120 three-vegetable plates
What is the range of the following list of ordered pairs?
(-3,-1), (0, -2), (4,3), (1,5)
Answers
Answer:
The range is 8.
Step-by-step explanation:
5-(-3)=8
For a two-sample t test where n1 = 16 and n2 = 12, what are the appropriate degrees of freedom?
Answers
The degrees of freedom for an independent t-test when n1 = 16 and n2 = 12 are 26.
Given,
n1 = 16
n2 = 12
Here,
An independent t-test, often known as a two-sample t-test, compares the means of two unrelated groups to see whether they are significantly different from each other. The t-test is an essential method that can help you determine whether or not a certain hypothesis is true, regardless of whether or not it is accurate.
Degree of freedom for independent t test: DF = (n1 + n2) - 2
DF = (16 + 12) - 2
DF = 26
Therefore, the degrees of freedom for an independent t-test when n1 = 16 and n2 = 12 are 26.
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Imagine you have the following results from a case-control study, stratified on two levels of some characteristic:
Stratum 1 OR = 0.333
Stratum 2 OR = 0.335
Crude OR = 0.334
These results are most consistent with the characteristic being
Select one:
a. Neither a confounder nor an effect modifier
b. A confounder, but not an effect modifier
c. An effect modifier
d. A bias
Answers
The correct answer to the question is option c) An effect modifier.
A case-control study is a type of observational study that compares two groups of individuals: those who have the disease or outcome under investigation (cases) and those who do not (controls).
It aims to determine if an exposure or risk factor is associated with the development of the disease or outcome.
In this case, the results of the study indicate that there is a difference in the odds ratio (OR) between the two strata, which suggests that the characteristic being studied is an effect modifier.
An effect modifier is a factor that modifies the effect of the exposure on the outcome and leads to different measures of association across different levels of the factor.
Therefore, the characteristic is an effect modifier as it leads to different ORs in the two strata.
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Anytown households that earn more than $75,000 tend to buy sports equipment, while households that earn less than $75,000 tend to buy TVs. Which new business would be most likely to succeed? a car dealership an electronics store an office supply store a sporting goods store.
Answers
Answer: An Electric Store
Step-by-step explanation: Hoped This Helped! Thx For The Points!
Answer:
B
Step-by-step explanation:
an electronics store
need help asap!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
PART A
The amount of snowfall and number of trucks is proportional.
Because the increase in snowfall, increases the number of trucks sent out as read from the table.
PART B
\( let \: the \: number \: of \: tracks \: be \: x\\ by \: linear \: extrapolation \\ \binom{inches \: \: \: \: 12 \: \: 18 \: \: 23}{trucks \: \: \: \: 30 \: \: 45 \: \: x} \\ \frac{23 - 12}{x - 30} = \frac{18 - 12}{45 - 30} \\ \frac{11}{x - 30} = \frac{6}{15} \\ 11 \times 15 = 6(x - 30) \\ 165 = 6x - 180 \\ 6x = 165 + 180 \\ 6x = 345 \\ x = 57.5 \\ x = 58 \: trucks \\ hence \: 58 \: trucks \: were \: sent \: out\)
Answer:
PART A
The amount of snowfall and number of trucks is proportional.
Because the increase in snowfall, increases the number of trucks sent out as read from the table.
PART B
Let the number of tracks be x
By linear extrapolation, we get
inches | 12 | 18 | 23
trucks | 30 | 45 | x
(23 - 12)/(x - 30) = (18 - 12)/(45 - 30)
(11)/(x - 30)=6/15
11×15 = 6(x - 30)
165 = 6x - 180
6x = 165 + 180
6x = 345
x = 57.5
x = 58 trucks
Hence, 58 trucks were sent out.
Write the negation of the following statement: ABC and DEC are
complementary angles.
A)OZABC and ZDEC are not complementary angles.
B)ZABC and ZDEC are supplementary angles.
C)The sum of ABC and ZDEC is 180 degrees.
D)The sum of ABC and ZDEC is 90 degrees.
Answers
Why?
Complementary angles: add up to 90 degrees.
Supplementary angles: add up to 180
degrees.
there is a 60% chance that fund b will rise in price given that fund a rises in price. there is also a 30% chance that fund b will rise in price. what is the probability that a rises and b does not rise in price?
Answers
The probability that a rises and b does not rise in price is: 24%
We can use conditional probability to solve this problem.
Let A = "fund a rises in price" and B = "fund b rises in price".
From the information provided, we know that:
P(B|A) = 0.6 (the probability that fund b rises in price given that fund a rises in price)P(B) = 0.3 (the probability that fund b rises in price)Using the formula for conditional probability, we can find the probability that a occurs and b does not occur:
P(A and B') = P(A) * P(B'|A)We don't know the probability of a, but we can find it using the formula for conditional probability and Bayes' theorem:
P(A) = P(B|A) * P(A) / P(B)Substituting in the known probabilities:
P(A) = 0.6 * P(A) / 0.3Solving for P(A), we get:
P(A) = 0.6Now we can use this value to find P(A and B'):
P(A and B') = P(A) * P(B'|A)P(A and B') = 0.6 * (1 - P(B|A))P(A and B') = 0.6 * (1 - 0.6)P(A and B') = 0.24So, the probability that fund a rises in price and fund b does not rise in price is 0.24 or 24%.
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Evaluate the expression (3 + m)^3 , when m=2
Answers
(3+2)^3
=5^3
=125
Answer:
the answerrrrrrrrrrr is 27+54m+36m^2+8m^3
Investors buy a studio apartment for $200,000 of this amount they have a down payment of $50,000 their down payment is what percent of the purchase price what percent of the purchase price would a $70,000 down payment be their down payment is what percent of the purchase price
Answers
Answer: 35%
Step-by-step explanation:
$70,000 was the down payment for a total price of $200,000.
Down payment percentage = 70,000 / 200,000
= 0.35
= 35%
What were the dimensions of the original lawn? 4 feet by 4 feet 8 + 6 startroot 2 endroot feet by 8 + 6 startroot 2 endroot 8 minus 6 startroot 2 endroot feet by 8 + 6 startroot 2 endroot 20 feet by 20 feet.
Answers
The dimensions of the original lawn were; 20 ft by 20 ft
What are the dimensions of the lawn?We are given that;
The equation (x – 8)² = 144
x represents the side measure of the original lawn
Since she reduces the size of her square grass lawn by 8 feet on each side. the area of the smaller lawn is 144 square feet;
We can find the side lengths by solving the given equation to get;
(x – 8)² = 144
Find the square root of both sides to get;
√(x – 8)² = √144
x - 8 = 12
x = 12 + 8
x = 20 ft
Thus, the dimensions are concluded to be 20 ft by 20 ft.
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Complete question is;
Jillian is trying to save water, so she reduces the size of her square grass lawn by 8 feet on each side. the area of the smaller lawn is 144 square feet. in the equation(x – 8)² = 144, x represents the side measure of the original lawn.what were the dimensions of the original lawn?
The graph of the function is of the form
f(x) = a * sin(kc – c) + h.
Answers
Explain
There 0,3 on the graph
You use this formula
f(x)=asin(kx-c)+h
and the maximum and minimum value of this function
a+ h and -a+ h
So a=3 and h=0
So we have
We have; f(x)= 3sin(kx - c)
and we have from the graph;
f(O)=3
So
Sin(-c) =-1
Therefore C=. Pi/ 2 +2pi n
We have period of the function is pi
2pi/ k
k=2
So it will equal Pi
Do you have any doubts ?
A solid with surface area 50units^2 is dilated by a scale factor of K to obtain a solid surface area 200units^2. Find the value of K.
Answers
The value of K is 2.
Let's denote the scale factor as K. The surface area of a solid after dilation is directly proportional to the square of the scale factor.
We are given that the initial surface area of the solid is 50 units^2, and after dilation, the surface area becomes 200 units^2.
Using the formula for the surface area, we have:
Initial surface area * (scale factor)^2 = Final surface area
50 * K^2 = 200
Dividing both sides of the equation by 50:
K^2 = 200/50
K^2 = 4
Taking the square root of both sides:
K = √4
K = 2
Therefore, the value of K is 2.
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Question Content Area
Net Present Value
A project has estimated annual net cash flows of $15,000 for ten
years and is estimated to cost $47,500. Assume a minimum acceptable
rate of return of 20%. Use
Answers
The required rate of return (or minimum acceptable rate of return) is 20 percent. If the net cash flows are $15,000 per year for ten years, the total cash flow is $150,000. The project's cost is $47,500. We can now apply the net present value formula to determine whether or not the project is feasible.
Net Present Value (NPV) = Cash flow / (1 + r)^n - Cost Where, r is the discount rate, n is the number of years, and Cost is the initial outlay.
Net Present Value = 150000 / (1 + 0.20)^10 - 47500
Net Present Value = $67,482.22
Since the NPV is positive, the project is feasible. When calculating net present value, it's important to remember that a positive NPV implies that the project is expected to generate a return that exceeds the cost of capital, whereas a negative NPV indicates that the project is expected to generate a return that is less than the cost of capital, and as a result, it should be avoided.
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The population of a city has been increasing by 2% annually. The sign shown is from the year 2000.
CITY LIMIT
BROOKFIELD
POP. 315,000
Write an exponential growth function that represents the population t years after 2000
What will the population be in 2020? Round your answer to the nearest thousand
The population will be about
Answers
The population will be about 2972 population in 2020
Exponential functionsThe standard exponential equation is expressed as;
y = ab^x
where
a is the interceptb is the initial populationx is the timeGiven the following parameters
a = 2000b = 0.02Substittute the given parameters into the formula
y = 2000(1.02)^x
If x = 20 (from 2000 to 2020)
The population will be expressed as;
y = 2000(1.02)^20
y = 2972 populations
Hence the population will be about 2972 population in 2020
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ill give brainliest n a recent survey, 3 out of every 5 students said Math is their favorite class.If 200 students were surveyed, how many students can be expected to choose math as their favorite class?Answer options with 4 optionsA.75B.80C.120D.125
Answers
Answer: D. 120 students
Step-by-step explanation:
This is an easy solution
Take 300 and divide it by 5
300/5
This will result in 40
Now Multiply 40 by 3
Like so: 40x3
This will result in 120
Answer:
C) 120
Step-by-step explanation:
Ratio - 3:5
200 times 3/5 = 120
Plz help! Sam had an appointment 90 miles away from home at 2pm. He drove there at 60 mph, and was 15 minutes late. What time did Sam start driving at?
Example: 1:50
Answers
Answer:
12:45 pm
Step-by-step explanation:
First we find out the amount of time it takes to drive 90 miles at 60 mph.
speed = distance/time
time * speed = distance
time = distance/speed
time = 90 miles / 60 mph
time = 1.5 hour = 90 minutes
It takes 1.5 hour, or 90 minutes, to drive 90 miles at a speed of 60 mph.
To get there at 2:00 pm, he should have left at 12:30 pm.
He got there 15 minutes late, so he must have left 15 minutes late.
He left at 12:45 pm.
Answer: 12:45 pm
the second box has options in it that say “in the center”, “on the left”, and "on the right”
Answers
Answer:
skew right;
most of the data is on the left (the start)
Step-by-step explanation:
Observing the data distribution in the leaf plot given, we would see that most of the data are occuring at the start. This can be referred to as a positively skewed data. The tail of the distribution (the thin side) is to the right.
Therefore, the shape can be described as SKEW RIGHT.